
\(|AA+AA| = \Omega ( \min \lbrace p, |A|^{3/2}\rbrace )\)  (Rudnev [1]}; see also [2]}, [3]}, [4]}).

\(|(A-A)^2+(A-A)^2| = \Omega (p)\)  when \(|A| > p^{2/3}\)  (Chapman, Erdoğan, Hart, Iosevich, and Koh [5]}; see also [6]}, [4]}).

\(|A+AA| = \Omega ( \min \lbrace p, |A|^{3/2}\rbrace )\)  (Roche-Newton, Rudnev, and Shkredov [8]}; see also [9]}, [4]}).

\(|A(A+A)| = \Omega ( \min \lbrace p, |A|^{3/2}\rbrace )\)  (Aksoy-Yazici, Murphy, Rudnev, and Shkredov [11]}; see also [4]}).

